Person 1 could likely have more than 10 blinks as there are 15 seconds (9*5 + 40 = 85s vs. 10*10 = 100s) unaccounted for if the test interval was 100s. This is assuming that the potential 11th blink for person 1 doesn't have a time greater than 15 seconds from the 10th, in which it would contribute to the next time interval.

I agree that the two methods are not the same. Here is an example that may be a little extreme, but is useful: Suppose you are tracking recordable injuries per month at your company location via process behavior charts. Some months there are zero injuries, some months there are 1, or 2, o3 , etc. If the average number of recordable injuries per month is low (< 6), then the data is "chunky" (see Dr. Donald Wheeler articles on Chunky data), and the control chart method does not yield yield useful results/conclusions. HOWEVER, if you track by "Days between recordable injuries", the control chart works quite well.

What is the distribution of the data? What does it matter? The I-MR chart does not require the data to have a particular distribution!

If ultimately trying to build regression models with lots of 'zeros' in the response variable set, there are a family of regression techniques known generically as 'zero inflated'. The zero inflated modeling capability is a part of JMP Pro in the Fit Model -> Generalized Regression personality, Distribution: ZI Binomial (and others). Here is a link to the relevant sections of the JMP online documentation as well: